Yes you can! Welcome to the Stan community.
You might find this post useful by the author of the {bmrs} package: Help with lasso example in brms - #7 by paul.buerkner
What you are looking for is called the Horsehoe Prior (Regularized horseshoe priors in brms — horseshoe • brms) which is better than the LASSO prior (Set up a lasso prior in brms — lasso • brms) in bayesian models.
Also see these references:
- Carvalho, C. M., Polson, N. G., & Scott, J. G. (2009). Handling Sparsity via the Horseshoe. Artificial Intelligence and Statistics, 73–80. http://proceedings.mlr.press/v5/carvalho09a.html
- Park, T., & Casella, G. (2008). The Bayesian Lasso. Journal of the American Statistical Association, 103(482), 681-686.
- Piironen, J., & Vehtari, A. (2017a). On the Hyperprior Choice for the Global Shrinkage Parameter in the Horseshoe Prior. Artificial Intelligence and Statistics, 905–913. http://proceedings.mlr.press/v54/piironen17a.html
- Piironen, J., & Vehtari, A. (2017b). Sparsity information and regularization in the horseshoe and other shrinkage priors. Electronic Journal of Statistics, 11(2), 5018–5051. https://doi.org/10.1214/17-EJS1337SI
- Ari Vehtari - Model assessment, selection and inference after selection
- Michael Betancourt — Bayes Sparse Regression